Consider a market in which there are two types of workers L and H. Each type of worker has a different level of productivity, but that productivity is unobservable ex ante to potential employers. Before seeking employment at a firm in the market, all workers can (if they choose) get some level of education e. This choice of education e is observable to all, including potential employers. Assume that the market is competitive, so expected profits must be zero in equilibrium. The L-type workers have a productivity of 2 if they work for a firm in the market. They also have an outside option of 2. The utility function of the L-type workers UL = wL - eL, where wL is the wage received and eL is the level of education they obtain. The H type worker has an outside option of 2 and a productivity of 4 if they are employed by a firm in the market. The utility function for a H-type worker is UH = wH - (1/3)eH, where wH is the wage paid to a H-type and eH is the education they choose to get. a. Find a separating equilibrium in which education is used as a signal of productivity. With the aid of a diagram, explain your answer. What is the maximum level of education the H-types will choose to get in any separating equilibrium? Explain your answer. (7 marks) b. Now assume that the utility function for the H-type workers is UH = (1/3).wH - (1/3)eH. Is there a separating equilibrium? If so, find it. If not, explain why. (3 marks) (Upload your scanned handwritten answer and submit via the Assignment folder.